BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

OG12 problem some easy steps to solve-reqd

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 62
Joined: Wed May 04, 2011 9:50 pm
Thanked: 2 times
Followed by:2 members

OG12 problem some easy steps to solve-reqd

by kishokbabu » Mon Jan 02, 2012 3:57 am
A school administrator will assign each student in
a group of n students to one of m classrooms. If
3 < m < 13 < n, is it possible to assign each of the
n students to one of the m classrooms so that each
classroom has the same number of students assigned
to it?

(1) It is possible to assign each of 3n students to
one of m classrooms so that each classroom
has the same number of students assigned to it.

(2) It is possible to assign each of 13n students to
one of m classrooms so that each classroom
has the same number of students assigned to it.
Top
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 425
Joined: Wed Dec 08, 2010 9:00 am
Thanked: 56 times
Followed by:7 members
GMAT Score:690

by LalaB » Mon Jan 02, 2012 9:26 am
discussed here -https://www.beatthegmat.com/a-school-adm ... 42237.html
and
here- https://www.beatthegmat.com/n-students-t ... ago-40-646

please let us know whether u still need an explanation even after reading all these posts
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 768
Joined: Wed Dec 28, 2011 4:18 pm
Location: Berkeley, CA
Thanked: 387 times
Followed by:140 members

by Mike@Magoosh » Mon Jan 02, 2012 9:38 am
Hi, there! I'm happy to help with this. :)

This is a deep conceptual question. I would say: think about translating from the situation into pure math terms.

Essentially, we are being asked: does m divide evenly in n? If m divides evenly into n, then the quotient n/m will be the exact number of students in each classroom. If m doesn't divide evenly into n, then when we divide, we will get a remainder, and when we put those "remainder" kids into the m classrooms, that will make some of the rooms have more students than others.

Statement #1 says that 3n is evenly divisible by m --- i.e. the quotient (3n)/m has no remainder. This could happen if n/m to begin with --- say n = 56 and m = 7 --- if m goes into n, it will go into 3n. Or, it could happen if m is divisible by 3 and another factor, and n is divisible only by this second factor --- for example, if m = 6 and n = 22, then m goes evenly into 3n = 66, but not into n. Because there are two cases, there's no way to decide whether m divides evenly into n. Statement #1 is not sufficient.

Statement #1 says that 13n is evenly divisible by m --- i.e. the quotient (13n)/m has no remainder. Here, there's no way that m has a factor of 13 in it, because we are told m < 13. Any factor of m greater than one will not divide into 13, because 13 is prime. Therefore, the only way m will divide evenly into 13n is if it divides evenly into n. This unambiguously answers the question. Therefore, Statement #2 is sufficient.

Answer = B

Does that make sense? Let me know if you have any questions.

Here's another problem about numbers & factors, just for practice:

https://gmat.magoosh.com/questions/308

Mike :)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Mon Jan 02, 2012 9:59 pm
kishokbabu wrote:A school administrator will assign each student in
a group of n students to one of m classrooms. If
3 < m < 13 < n, is it possible to assign each of the
n students to one of the m classrooms so that each
classroom has the same number of students assigned
to it?

(1) It is possible to assign each of 3n students to
one of m classrooms so that each classroom
has the same number of students assigned to it.

(2) It is possible to assign each of 13n students to
one of m classrooms so that each classroom
has the same number of students assigned to it.
The question can be rephrased as "If 3 < m < 13 < n, is n/m an integer?"

(1) The information in statement 1 implies that 3n/m is an integer. Now we have find whether n/m is an integer.
Given that 3 < m < 13 < n, if n = 36 and m = 6, then n/m is an integer.
On the other hand if n = 40 and m = 6, then n/m is not an integer.
Since we don't get a unique answer, so (1) is NOT SUFFICIENT.

(2) According to the statement, 13n/m is an integer.
3 < m < 13 < n implies that m lies between 3 and 13 but is not 13, so 13n/m can be integer only if n/m is an integer.
So, (2) is SUFFICIENT.

The correct answer is B.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Master | Next Rank: 500 Posts
Posts: 382
Joined: Thu Mar 31, 2011 5:47 pm
Thanked: 15 times

by ArunangsuSahu » Tue Jan 03, 2012 7:18 pm
Statement (A)

Let's take the following cases:
n=36, m=6...HOLDS GOOD

n=40, m=6...n/m is not an integer.
INSUFFICIENT

Statement (B)

as 3<m<13 for 13n/m to be an integer...n/m has to be an integer...SUFFICIENT
Top
Post new topic Post Reply
• Page 1 of 1